【作者】 王亮；

【导师】 寿永熙；

【作者基本信息】 内蒙古工业大学 ， 计算机应用技术， 2007， 硕士

【摘要】 CT图像重建是图像处理的一个重要分支,它既包含数学理论基础研究,又涉及实际的应用领域。近年来,CT图像重建在医学诊断、工业无损检测、农林业、地球物理和环境保护等领域都发挥了重要作用。CT图像重建算法可以分为两类,解析变换法和代数迭代法。解析变换法重建速度快,重建效果也好,但是要求投影数据是完全的。而代数迭代法首先就将基本公式进行离散化,从而把解析法求反问题转换成代数方程组的求解问题。代数迭代法简单,可以应用于不完全投影数据的图像重建问题。图像重建的离散化模型中,投影射线间具有几何对称结构,这种几何对称结构与像素点值和物体的密度分布无关。将这种对称性结构应用到代数迭代重建算法中,引出了对称块迭代算法。对称块迭代算法改变了传统代数迭代算法的迭代格式和迭代顺序,有效地加快了重建速度,提高了重建图像的质量。本文将对称性结构引入动态松弛因子迭代和随机迭代过程中,提出了对称块动态松弛因子迭代法和对称块随机迭代法。这两种算法将逐线选取动态松弛因子和逐线进行随机迭代调整为按对称块选取动态松弛因子,以及按对称块进行随机迭代。此外,针对重建图像边界效果较差的问题,本文提出了像素分析法来确定边界,即在边界点处采用不同的松弛因子,可以使重建结果中的边界变得更清晰。对于实测数据和模拟数据,分别采用对称块动态松弛因子迭代法、对称块随机迭代法,以及像素分析法进行图像重建数值实验。重建图像与经典算法重建结果作比较,并对误差指标作分析。数值实验的结果表明:改进后的算法提高了重建速度,改善了成像精度。更多还原

【Abstract】 The Computerized Tomography (CT) is an important branch of Image Processing. It contains basic research of mathematics theory and is related to actual applied domains. In recent years, CT has been widely applied in many fields such as medical diagnosis, industrial non-destructive testing, agriculture and forestry, physical geography and environmental protection.CT Image Reconstruction includes the analytic method and iterative method. The analytic method is fast and good quality, but request projection data is complete. The algebraic method partitions the basic formula firstly. And then transform the analytic method into algebraic equation set. The algebraic method is simple, and also may process incomplete data.There exists geometric symmetric structure between project radials in the discrete model. This structure is independent of pixel value and the density distributing of object. Symmetric block iterative algorithm technique (SBIRT) was produced when the symmetric structure is applied in algebraic algorithm. Symmetric block iterative algorithm technique changed iterative mode and order of the traditional algorithm, sped up the reconstruction speed, and improved the quality of images.In this paper, we bring the symmetric block structure into dynamic flabby coefficient and radon iterative, produce symmetric block dynamic flabby coefficient and symmetric block radon iterative which change the line-by-line iterative mode. Meanwhile, aiming at the boundary dimness we put forward pixel analyze to confirm the boundary. At the point of boundary we adopt different flabby coefficient to make the borderline more clearly.We use actual data and simulated data to experiment by the method of symmetric block dynamic flabby coefficient technique, symmetric block random iterative and pixel analyze. Compare the reconstructed images by our methods and traditional methods, and make analyze of evaluate parameter. The result indicates that the improved algorithms not only increase the reconstruction speed but also improve the reconstruction precision.更多还原